In the figure given below ABC is a rightangled triangle where A 90o AB p cm and AC q cm On the three...........

Quantitative Aptitude (CDS) Mensuration 2D

In the figure given below, ABC is a rightangled triangle where $\small \angle$ A = 90^o ,AB = p cm and AC = q cm. On the three sides as diameters semicircles are drawn as shown in the figure. The area of the shaded portion, in square cm, is

$\small \pi$ (p² + q² ) / 2

$\small \pi$ (p² + q² )

pq/2

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Explanation:

Shaded area = area of semi circles with dia AB & AC + area of triangle ABC – area of of semi circle with dia BC.
= ( $\small \pi$ p² )/ 8 + ( $\small \pi$ q² )/ 8 + 1/2pq - ( $\small \pi$ BC² ) / 8....................(i)
Now , in triangle ABC
AB² + AC² = BC² = p² + q²
Putting BC² in above equation (i)
Shaded Area = ( $\small \pi$ p² )/ 8 + ( $\small \pi$ q² )/ 8 + 1/2pq - ( $\small \pi$ (p² + q²) / 8
=pq/2